research-direction: empirically test whether NQS feedback escapes the Mazzola coupon-collector flaw (thin niche)

[thc1006]

TL;DR

Mazzola et al. JCTC 2025 proved QSCI/SQD has fatal "coupon collector" sampling inefficiency — repeatedly samples same configs, fails to find rare-but-important ones. They tested flat quantum sampling. Our HI-NQS-SQD has iterative NQS feedback. Question: does iterative feedback shift the coupon-collector regime? Empirically untested in literature.

TL;DR-2

We have data already that can answer this. Need: 1 small analysis paper + 2-3 supplementary jobs.

Background

Mazzola critique:

• QSCI sample distribution = ground state amplitude squared
• Coupon collector with skewed distribution → coverage cost grows superpolynomially
• Sample wastage on already-seen configs
• QSCI expansions less compact than classical SCI heuristics
• Tested on N2 and [2Fe-2S]

Hypothesis (untested in literature)

HI-NQS-SQD iterates: NQS resampled at each iter from updated eigenvector marginals. This changes the underlying sampling distribution iteratively.

Three possible outcomes:

• (A) Escapes Mazzola: NQS focus → polynomial (or sub-Mazzola-power) scaling of unique determinants per iter
• (B) Worse than Mazzola: NQS over-focuses → misses rare configs faster than flat sampling
• (C) Equivalent: Iterative feedback adds nothing fundamental

Available data (already in our hands)

• 52Q-AUGMENT: per-iter n_unique_new trajectory for NQS feedback case
• 52Q-N5K-Random: per-iter n_unique_new for flat random sampling (baseline)
• Per-iter coeff_histogram showing |c|² tail dynamics

These let us plot:

• log(n_unique_per_iter) vs iter for NQS vs random
• Coupon-collector signature comparison
• Compactness comparison (n_configs to reach given accuracy)

What's missing

• N2-CAS-12 / 15 / 17 jobs to fill scaling axis (small CAS faster, ~30 min each on H200)
• Cr2 datapoint (multireference contrast)
• Standardized analysis script

Output: short workshop paper

Title: "Iterative neural-network feedback in NQS-SQD pipelines: does it escape the QSCI sampling bottleneck?"

• ~6 pages
• Clear hypothesis + falsification framework
• Empirical analysis of our existing + small new data
• Either confirms Mazzola applies + provides empirical scaling exponents, or shows escape
• Workshop venue (NeurIPS ML4Sci, AAAI QSciML, etc.)

What this is NOT

Not a new method paper. Not a chem-acc claim. A specific case-study within the Mazzola framework. Modest contribution but original empirical observation.

Risk

• Result could be uninteresting (exact equivalence to Mazzola for our pipeline)
• Other groups may publish similar analysis first — monitor arXiv
• Reviewers may say "case study insufficient" — counter with "Mazzola critique demanded empirical follow-up"

Effort: 6-8 weeks

• 1 week: standardize analysis on existing data
• 2 weeks: run supplementary jobs (CAS-12/15/17/Cr2)
• 2-3 weeks: writing + figures

Dependency

• Issue research-positioning: HI-NQS-SQD is not a novel method — it's a composition of established techniques. Document accordingly. #50 (positioning audit) confirms this is best fit for our work scope
• Issue research-direction: cross-method benchmark at fixed compute budget on N2/Cr2 active-space series (only realistic publishable angle) #51 (benchmark) may absorb this if expanded